Technique for factoring uncertainty into cost-based query optimization

ABSTRACT

A technique for factoring uncertainty into cost-based query optimization includes: determining the degree of uncertainty involved in the cost estimates for the query, determining the degree of sensitivity the query has to that uncertainty, and determining if there is an access path that performs well across the range of possible conditions that could occur at execution time, reducing the risk of performance spikes and performance volatility. If such an access path exists, select that access path; if not, perform parametric query optimization or query re-optimization.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates in general to database management systemsperformed by computers, and in particular, to a technique for factoringuncertainty into cost-based query optimization.

2. Description of Related Art

Computer systems incorporating Relational DataBase Management System(RDBMS) software using a Structured Query Language (SQL) interface arewell known in the art. The SQL interface has evolved into a standardlanguage for RDBMS software and has been adopted as such by both theAmerican National Standards Institute (ANSI) and the InternationalStandards Organization (ISO).

An important aspect of the RDBMS software is the optimization of the SQLqueries. Typically, the RDBMS software will include a cost-basedoptimizer function that chooses among a plurality of possible accesspaths in order to select an optimal query execution plan. Choosingsub-optimal query execution plans can be detrimental for queryperformance.

Cost-based query optimizers must sometimes make assumptions about thedata being queried. The assumptions typically are:

-   -   Uniform data distribution, and    -   Independence amongst predicate conditions.

However, these assumptions will not always be true. Often, the data willnot be uniformly distributed and there will be correlation amongst thespecified predicate conditions. The assumptions, therefore, lead touncertainty that the cost estimate computed by the optimizer isaccurate. Naturally, if the cost estimate is not accurate, the selectedaccess path may perform poorly.

Typically, cost-based query optimizers attempt to deal with thisuncertainty by eliminating it whenever possible. This is usuallyaccomplished through the collection of detailed statistics, and perhapsthrough the use of statistical views, statistics advisors, feedbackmechanisms, or other means.

When the query involves predicates with host-variables, i.e., data itemsdeclared in an SQL statement with their values determined at runtime,collecting additional statistics may do little to reduce theuncertainty. In these cases, traditional cost-based query optimizers maydefer the optimization until execution time, when the host-variablevalues are known, or use techniques to feed back information from priorexecutions of the query (i.e., the “learning optimizer” technique) inorder to improve the accuracy of the cost-estimates made by the queryoptimizer over many executions of the query.

While eliminating, or minimizing, the degree of uncertainty involved inestimating the cost of performing a particular query is desirable, itcannot always be achieved, and often the cost associated withidentifying and collecting the statistics needed to significantly reduceuncertainty, or the cost of learning the execution properties of thequery to the extent needed to more accurately optimize the query, can beextremely high.

Thus, there is a need in the art for improved optimization techniquesthat ensure the selection of optimal (or near optimal) access paths forqueries using cost-based optimization. Specifically, there is a need inthe art for solutions to problems directed to the selection of optimalplans using a technique for factoring uncertainty into cost-based queryoptimization.

SUMMARY OF THE INVENTION

To overcome the limitations in the prior art described above, and toovercome other limitations that will become apparent upon reading andunderstanding the present specification, the present invention disclosesa method, apparatus, and article of manufacture for optimizing a queryin a computer system, which is a technique for factoring uncertaintyinto cost-based query optimization. The present invention includes:determining the degree of uncertainty involved in the cost estimates forthe query, determining the degree of sensitivity the query has to thatuncertainty, and determining if there is an access path that performswell across the range of possible conditions that could occur atexecution time, reducing the risk of performance spikes and performancevolatility. If such an access path exists, select that access path; ifnot, perform parametric query optimization or query re-optimization.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers representcorresponding parts throughout:

FIG. 1 illustrates an exemplary computer hardware and softwareenvironment that could be used with an embodiment of the presentinvention;

FIG. 2 is a flowchart illustrating the steps necessary for theinterpretation and execution of SQL statements in an interactiveenvironment according to an embodiment of the present invention;

FIG. 3 is a flowchart illustrating the steps necessary for theinterpretation and execution of SQL statements embedded in source codeof a host language according to an embodiment of the present invention;and

FIG. 4 is a flowchart illustrating the logic of the method for queryoptimization according to the preferred embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In the following description of the preferred embodiment, reference ismade to the accompanying drawings, which form a part hereof, and inwhich is shown by way of illustration a specific embodiment in which theinvention may be practiced. It is to be understood that otherembodiments may be utilized and structural and functional changes may bemade without departing from the scope of the present invention.

Overview

The present invention proposes a different approach from the prior art:one that recognizes that uncertainty is inherent in cost-based queryoptimization and factors that uncertainty into the access path selectionprocess. The result is a cost-based query optimizer that selects accesspaths that perform well across a range of possible conditions, providingmore consistent performance results, even in the presence of highuncertainty.

The present invention also enables the cost-based query optimizer torecognize and target those queries for which there is not a single planthat performs well across the range of possible conditions. Thosequeries can be optimized using techniques such as parametric queryoptimization, which selects multiple access paths for the query ratherthan a single access path and routes control to the appropriate accesspath at execution time based on the execution parameters of the query,or query re-optimization, which defers determining the access path untilexecution time when the execution parameters are known.

Some papers have been written which discuss the idea of viewingpredicate selectivity as a probability distribution rather than a singleselectivity estimate, but they require preprocessing to compute theprobability distribution from a random sample, or additional processingduring optimization to construct samples on the fly, or feedback fromprevious executions of the query to determine the probabilitydistribution. In all of these cases, there is high overhead involved inobtaining the probability distribution. Additionally, the probabilitydistribution itself is also prone to uncertainty, and techniques thatrely on cost estimates based upon probability distributions may stillexperience erratic performance behavior.

The present invention avoids the costly overhead associated withprobability distributions, and also avoids being dependent on accurateprobability distribution values, in order to select the best plan for arange of possible conditions. It also can identify and target thosequeries that are best suited to parametric query optimization or otheroptimization techniques without incurring the high over-head associatedwith probability distributions.

Hardware and Software Environment

FIG. 1 illustrates an exemplary computer hardware and softwareenvironment that could be used with the present invention. In theexemplary environment, a server system 100 is connected to one or moreclient systems 102, in order to manage one or more databases 104 and 106shared among the client systems 102.

Operators of the client systems 102 use a standard operator interface108 to transmit commands to and from the server system 100 thatrepresent commands for performing various search and retrievalfunctions, termed queries, against the databases. In the presentinvention, these queries conform to the Structured Query Language (SQL)standard, and invoke functions performed by Relational DataBaseManagement System (RDBMS) software. In one embodiment of the presentinvention, the RDBMS software comprises the DB2 product offered by IBMCorporation, the assignee of the present invention. Those skilled in theart will recognize, however, that the present invention has applicationto any RDBMS software.

As illustrated in FIG. 1, the RDBMS includes three major components: theResource Lock Manager (RLM) 110, the Systems Services module 112, andthe Database Services module 114. The RLM 110 handles locking services,because the RDBMS treats data as a shared resource, thereby allowing anynumber of users to access the same data simultaneously, and thusconcurrency control is required to isolate users and to maintain dataintegrity. The Systems Services module 112 controls the overall RDBMSexecution environment, including managing log data sets 106, gatheringstatistics, handling startup and shutdown, and providing managementsupport.

At the heart of the RDBMS architecture is the Database Services module114. The Database Services module 114 contains several submodules,including a Relational Database System (RDS) 116, Data Manager 118,Buffer Manager 120, and SQL Interpreter 122. These submodules supportthe functions of the SQL language, i.e., definition, access control,retrieval, and update of user and system data.

Generally, each of the components, modules, and submodules of the RDBMScomprises instructions and/or data, and are embodied in or retrievablefrom a computer-readable device or medium, e.g., a memory, a datastorage device, a remote device coupled to the server computer 100 by adata communications device, etc. Moreover, these instructions and/ordata, when read, executed, and/or interpreted by the server computer100, cause the server computer 100 to perform the steps necessary toimplement and/or use the present invention.

Thus, the present invention may be implemented as a method, apparatus,or article of manufacture using standard programming and/or engineeringtechniques to produce software, firmware, hardware, or any combinationthereof. The term “article of manufacture”, or alternatively, “computerprogram product”, as used herein is intended to encompass a computerprogram accessible from any computer-readable device or media.

Of course, those skilled in the art will recognize many modificationsmay be made to this configuration without departing from the scope ofthe present invention. Specifically, those skilled in the art willrecognize that any combination of the above components, or any number ofdifferent components, including computer programs, peripherals, andother devices, may be used to implement the present invention, so longas similar functions are performed thereby.

Interactive SQL Execution

FIG. 2 is a flowchart illustrating the steps necessary for theinterpretation and execution of SQL statements in an interactiveenvironment according to the present invention. Block 200 represents theinput of SQL statements into the server system 100. Block 202 representsthe step of compiling or interpreting the SQL statements in the RDBMS. Acost-based optimizer function within the RDBMS may transform or optimizethe SQL query in a manner described in more detail later in thisspecification. Generally, the SQL statements received as input specifyonly the desired data, but not how to retrieve the data. This stepconsiders both the available access paths (indexes, sequential reads,etc.) and system held statistics on the data to be accessed (the size ofthe table, the number of distinct values in a particular column, etc.),to choose what it considers to be the most efficient access path for thequery. Block 204 represents the step of generating a compiled set ofruntime structures called a query execution plan from the compiled SQLstatements, wherein each query execution plan represents a differentaccess path. Block 206 represents the execution of the plan and Block208 represents the output of the results.

Embedded/Batch SQL Execution

FIG. 3 is a flowchart illustrating the steps necessary for theinterpretation and execution of SQL statements embedded in source codeaccording to the present invention. Block 300 represents program sourcecode containing a host language (such as COBOL or C) and embedded SQLstatements. The program source code is then input to a pre-compile step302. There are two outputs from the pre-compile step 302: a modifiedsource module 304 and a Database Request Module (DBRM) 306. The modifiedsource module 304 contains host language calls to the RDBMS, which thepre-compile step 302 inserts in place of SQL statements. The DBRM 306 iscomprised of the SQL statements from the program source code 300. Acompile and link-edit step 308 uses the modified source module 304 toproduce a load module 310, while an optimize and bind step 312 uses theDBRM 306 to produce a compiled set of runtime structures for the queryexecution plan 314. As indicated above in conjunction with FIG. 2, theSQL statements from the program source code 300 specify only the desireddata, but not how to retrieve the data. The optimize and bind step 312may represent a cost-based optimizer function within the RDBMS thatoptimizes the SQL query in a manner described in more detail later inthis specification. Thereafter, the optimize and bind step 312 considersboth the available access paths (indexes, sequential reads, etc.) andsystem held statistics on the data to be accessed (the size of thetable, the number of distinct values in a particular column, etc.), tochoose what it considers to be the most efficient plan for the query.The load module 310 and plan 314 are then executed together at step 316.

Description of the Optimization Technique

The present invention discloses an improved optimization technique thatis typically performed at step 202 of FIG. 2 or step 312 of FIG. 3.Specifically, the present invention discloses a technique for factoringuncertainty into cost-based query optimization.

Factoring Uncertainty into Cost-Based Query Optimization

The core idea of the present invention is to give the cost-based queryoptimizer function of the RDBMS knowledge about the degree ofuncertainty involved in its cost estimates, and knowledge about thedegree of sensitivity that the query has to that uncertainty. With thatknowledge, the cost-based query optimizer is then enabled to choose anaccess path that performs well across the range of possible conditionsthat could occur at execution time, reducing the risk of performancespikes and performance volatility. Moreover, with that knowledge, thecost-based query optimizer is also enabled to recognize queries that arewell suited to parametric query optimization or query re-optimization,and automatically perform those optimization techniques on thosequeries.

Generally, the present invention involves the following steps:

-   -   Determine the degree of uncertainty involved in the query,    -   Determine the degree of sensitivity the query has to the        uncertainty,    -   Determine if there is a single access path that performs well        across the range of possible conditions,    -   If such an access path exists, select that access path; if not,        perform parametric query optimization or query re-optimization.

Determine the Degree of Uncertainty

To determine the degree of uncertainty, the cost-based query optimizeris extended such that it considers not just one set of assumptions aboutthe underlying data, but multiple assumptions. That is, in addition toestimating the cost of the query using the “normal” or standardassumptions of “uniform data distribution” and “independence ofpredicate conditions,” the optimizer will also estimate the cost of thequery using “pessimistic” and “optimistic” assumptions about the data.

Pessimistic assumptions include (but are not limited to):

-   -   Positive data skew (i.e., where the data is skewed toward the        predicate conditions), and    -   Positive correlation among predicate conditions (i.e., if one        predicate condition evaluates as “TRUE,” then other predicate        conditions also tend to evaluate as “TRUE”).

Optimistic assumptions include (but are not limited to):

-   -   Negative data skew (i.e., where data is skewed away from the        predicate conditions), and    -   Negative correlation among predicate conditions (i.e., if one        predicate condition evaluates as “TRUE,” then other predicate        conditions tend to evaluate as “FALSE”).

Pessimistic assumptions result in estimates that predict more rows willbe qualified by the query, while optimistic assumptions result inestimates that predict fewer rows will be qualified by the query.

Note that these assumptions can be characterized as “selectivitymodels,” namely a normal selectivity model, an optimistic selectivitymodel and a pessimistic selectivity model, in one embodiment of theinvention. However, the present invention is not limited to just thesethree models. Instead, there could be an arbitrary number of selectivitymodels that are used to cost queries. Moreover, these selectivity modelscan represent any set of selectivity assumptions. The choice of normal,optimistic and pessimistic selectivity models in this embodiment is forillustration only, as giving the most generic coverage of possibleoutcomes, but other selectivity models, and combinations of selectivitymodels, which may be based on heuristics, monitoring, statisticalanalysis, etc., could be used in place of, or in addition to, thenormal, optimistic and pessimistic selectivity models described herein.

When the cost-based query optimizer evaluates the query from theperspectives of chosen selectivity models, it gives the optimizer aclearer picture as to how each candidate access path being consideredperforms under the conditions associated with those selectivity models.

For example, consider the following table, which describes a resulting“cost-matrix” for access paths associated with plans ‘A’, ‘B’ and ‘C’:

Normal Pessimistic Optimistic Selectivity Selectivity SelectivityAssumptions Assumptions Assumptions Plan A - Cost of Cost of Cost ofBest plan using Plan A using Plan A using Plan A using normal normalpessimistic optimistic assumptions assumptions assumptions assumptionsPlan B - Cost of Cost of Cost of Best plan using Plan B using Plan Busing Plan B using pessimistic normal pessimistic optimistic assumptionsassumptions assumptions assumptions Plan C - Cost of Cost of Cost ofBest plan using Plan C using Plan C using Plan C using optimistic normalpessimistic optimistic assumptions assumptions assumptions assumptions

From the cost-matrix, plans A, B and C can be compared to see which oneperforms best across the range of selectivity models or assumptions.

Note that, when doing this comparison, the selectivity assumptions canbe weighted differently. That is, more weight can be given to the normalselectivity assumptions and less weight to the pessimistic andoptimistic selectivity assumptions. This accounts for the possibilitythat the normal selectivity assumptions are more likely to occur thanthe pessimistic or optimistic selectivity assumptions.

The degree of uncertainty for a particular access path can be calculatedas the difference between the normal, pessimistic, and optimisticestimated costs for that access path. The greater the difference incost, the greater the degree of uncertainty. The smaller the difference,the smaller the degree of uncertainty.

For example, consider the following costs for access paths associatedwith plans ‘A’, B′ and ‘C’:

Normal Pessimistic Optimistic Selectivity Selectivity SelectivityAssumptions Assumptions Assumptions Uncertainty Plan A - Cost = 1E+3Cost = 1E+5 Cost = 1E+2 9.99E+004 best plan using normal selectivityPlan B - Cost = 4E+3 Cost = 5E+3 Cost = 1E+3 4.00E+003 best plan usingleast pessimistic uncertain selectivity Plan C - Cost = 2E+3 Cost = 1E+7Cost = 5E+1 9.99E+006 best plan using most optimistic uncertainselectivity Sensitivity 3.00E+003 9.99E+006 9.50E+001 most leastsensitive sensitive

The estimated costs for plan ‘A’ range from 1E+2 to 1E+5; the estimatedcosts for plan ‘B’ range from 1E+3 to 5E+3 (smallest degree ofuncertainty); and the estimated costs for plan ‘C’ range from 5E+1 to1E+7 (largest degree of uncertainty). This shows a high degree ofuncertainty across the competing access path choices.

Determine the Degree of Sensitivity

The degree of sensitivity that a query has to the uncertainty about thecost of a particular plan can be calculated as the difference betweenthe costs of different access paths for the same selectivity assumption.

Using the example above: sensitivity under normal assumptions range from1E+3 to 4E+3 sensitivity under pessimistic assumptions range from 5E+3to 1E+7 (most sensitive); and sensitivity under optimistic assumptionsrange from 5E+1 to 1E+3 (least sensitive). This shows a high level ofsensitivity within the query, especially within the pessimisticselectivity model.

The following table describes the relationship between uncertainty andsensitivity:

Low uncertainty High uncertainty Low sensitivity Stable Stable Highsensitivity Stable Unstable

The table shows that a query may have high uncertainty, but if the queryis not sensitive to that uncertainty, then the uncertainty is not aproblem.

An example would be a query with the following predicate: “AGE<?”. Thistype of predicate typically has high uncertainty because the value ofthe parameter marker “?” is not known until execution time. Thepredicate may qualify all rows or no rows, and the query optimizer doesnot know which will occur at execution time (hence, there is highuncertainty). However, if there is no index on AGE, and the table is notjoined to any other table, then that uncertainty may not have any impacton the query, because that predicate is not critical to any of thecompeting access paths.

These cases typically do not benefit from attempts to reduce theuncertainty, and so there is no need to consider statistical views or astatistics advisor to eliminate the uncertainty. Likewise, these casesdo not benefit from parametric query optimization or queryre-optimization, because knowing the execution parameters does not helpthe optimizer select a better access path.

The table shows that those queries with high uncertainty and highsensitivity are the cases where statistical views and a statisticsadvisor should be considered. Those queries with high uncertainty andhigh sensitivity are also the cases where parametric query optimization,or query re-optimization may be highly beneficial.

Logic of the Cost-Based Query Optimizer

FIG. 4 is a flow chart that illustrates the logic performed by thecost-based query optimizer function of the RDBMS according to oneembodiment of the present invention. Specifically, the flow chartillustrates a method of generating an optimal access path to data for aquery.

Block 400 represents the RDBMS generating a plurality of access pathsfor the query.

Block 402 represents the RDBMS determining an uncertainty for the query,wherein the uncertainty is the difference between selectivityassumptions about the costs for each of the access paths. For example,the uncertainty may be the difference between normal, pessimistic oroptimistic selectivity assumptions about the costs for the access path.

As noted above, the normal selectivity assumptions may comprise uniformdata distribution or independence of predicate conditions; thepessimistic selectivity assumptions may comprise positive data skew(where data is skewed toward predicate conditions) or positivecorrelation among predicate conditions (such that, if one predicatecondition evaluates as true, then other predicate conditions also tendto evaluate as true); and the optimistic selectivity assumptions maycomprise negative data skew (where data is skewed away from predicateconditions) or negative correlation among predicate conditions (suchthat, if one predicate condition evaluates as true, then other predicateconditions tend to evaluate as false). Generally, the pessimisticselectivity assumptions result in estimates that predict more rows willbe qualified by the query, while the optimistic selectivity assumptionsresult in estimates that predict fewer rows will be qualified by thequery.

Moreover, the selectivity assumptions may be weighted differently. Forexample, the normal, pessimistic or optimistic selectivity assumptionsmay be weighted differently, with more weight given to the normalselectivity assumptions and less weight given to the pessimistic andoptimistic selectivity assumptions.

Block 404 represents the RDBMS determining a sensitivity of the query tothe uncertainty, wherein the sensitivity is the difference between thecosts of the access paths for the selectivity assumptions. For example,the sensitivity may be the difference between the costs of the accesspaths for the normal, pessimistic and optimistic selectivityassumptions.

Block 406 represents the RDBMS selecting one of the access pathsaccording to the uncertainty and the sensitivity. Specifically, thisBlock determines if there is a single access path that performs wellacross the range of possible conditions. If such an access path exists,then that access path is selected; if not, then parametric queryoptimization or query re-optimization may be performed at a later time.

Thereafter, the logic terminates.

Summary

In summary, the approach described in the present invention, extendingcost-based query optimization to factor uncertainty into the access pathselection process, is a simple and yet powerful and elegant solution fordealing with the uncertainty that is inherent in cost-based queryoptimization. It does not require expensive, and possibly wasteful,prior analysis of the workload in order to create statistical views orcollect detailed statistics in attempts to eliminate uncertainty. Italso does not require preprocessing to sample and compute probabilitydistributions. It simply enables the optimizer to recognize that theassumptions it makes may not be accurate in all cases, and that byconsidering other assumptions, and viewing the query from multipleperspectives, better performing access paths can be selected that areless likely to suffer performance spikes or perform erratically acrossmany executions of the query.

CONCLUSION

This concludes the description of the preferred embodiment of theinvention. The following describes some alternative embodiments foraccomplishing the present invention. For example, any type of computer,such as a mainframe, minicomputer, or personal computer, could be usedwith the present invention. In addition, any software program performingdatabase queries could benefit from the present invention.

In summary, the present invention discloses a method, apparatus, andarticle of manufacture for optimizing a query in a computer system,which includes a technique for factoring uncertainty into cost-basedquery optimization.

The foregoing description of the preferred embodiment of the inventionhas been presented for the purposes of illustration and description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed. Many modifications and variations are possiblein light of the above teaching.

What is claimed is:
 1. An apparatus for generating an optimal accesspath to data for a query being performed by a computer system toretrieve data from a database stored in a data storage device coupled tothe computer system, the apparatus comprising: (a) a computer systemhaving a data storage device coupled thereto, the data storage devicestoring data in a database; and (b) a relational database managementsystem performed by the computer system, the relational databasemanagement system configured for: generating a plurality of access pathsfor the query; determining an uncertainty for the query, wherein theuncertainty is the difference between selectivity assumptions about thecosts for each of the access paths; determining a sensitivity of thequery to the uncertainty, wherein the sensitivity is the differencebetween the costs of the access paths for the selectivity assumptions;and selecting one of the access paths according to the uncertainty andthe sensitivity; wherein the selectivity assumptions comprise normal,pessimistic or optimistic selectivity assumptions, the uncertainty isthe difference between the normal, pessimistic or optimistic selectivityassumptions about the costs for each of the access paths, and thesensitivity is the difference between the costs of the access paths forthe normal, pessimistic or optimistic selectivity assumptions.
 2. Theapparatus of claim 1, wherein the normal selectivity assumptionscomprise uniform data distribution.
 3. The apparatus of claim 1, whereinthe normal selectivity assumptions comprise independence of predicateconditions.
 4. The apparatus of claim 1, wherein the pessimisticselectivity assumptions comprise positive data skew where data is skewedtoward predicate conditions.
 5. The apparatus of claim 1, wherein thepessimistic selectivity assumptions comprise positive correlation amongpredicate conditions, such that, if one predicate condition evaluates astrue, then other predicate conditions also tend to evaluate as true. 6.The apparatus of claim 1, wherein the pessimistic selectivityassumptions result in estimates that predict more rows will be qualifiedby the query.
 7. The apparatus of claim 1, wherein the optimisticselectivity assumptions comprise negative data skew where data is skewedaway from predicate conditions.
 8. The apparatus of claim 1, wherein theoptimistic selectivity assumptions comprise negative correlation amongpredicate conditions, such that, if one predicate condition evaluates astrue, then other predicate conditions tend to evaluate as false.
 9. Theapparatus of claim 1, wherein the optimistic selectivity assumptionsresult in estimates that predict fewer rows will be qualified by thequery.
 10. The apparatus of claim 1, wherein the normal, pessimistic andoptimistic selectivity assumptions are weighted differently, with moreweight given to the normal selectivity assumptions and less weight givento the pessimistic and optimistic selectivity assumptions.
 11. Anarticle of manufacture comprising a computer readable storage mediumencoded with computer program instructions which, when accessed by acomputer system storing data in a database, cause the computer system tooperate as a specially programmed computer system, executing a method ofgenerating an optimal access path to data for a query being performed bythe computer system to retrieve data from the database, the methodcomprising: generating a plurality of access paths for the query;determining an uncertainty for the query, wherein the uncertainty is thedifference between selectivity assumptions about the costs for each ofthe access paths; determining a sensitivity of the query to theuncertainty, wherein the sensitivity is the difference between the costsof the access paths for the selectivity assumptions; and selecting oneof the access paths according to the uncertainty and the sensitivity;wherein the selectivity assumptions comprise normal, pessimistic oroptimistic selectivity assumptions, the uncertainty is the differencebetween the normal, pessimistic or optimistic selectivity assumptionsabout the costs for each of the access paths, and the sensitivity is thedifference between the costs of the access paths for the normal,pessimistic or optimistic selectivity assumptions.
 12. The article ofclaim 11, wherein the normal selectivity assumptions comprise uniformdata distribution.
 13. The article of claim 11, wherein the normalselectivity assumptions comprise independence of predicate conditions.14. The article of claim 11, wherein the pessimistic selectivityassumptions comprise positive data skew where data is skewed towardpredicate conditions.
 15. The article of claim 11, wherein thepessimistic selectivity assumptions comprise positive correlation amongpredicate conditions, such that, if one predicate condition evaluates astrue, then other predicate conditions also tend to evaluate as true. 16.The article of claim 11, wherein the pessimistic selectivity assumptionsresult in estimates that predict more rows will be qualified by thequery.
 17. The article of claim 11, wherein the optimistic selectivityassumptions comprise negative data skew where data is skewed away frompredicate conditions.
 18. The article of claim 11, wherein theoptimistic selectivity assumptions comprise negative correlation amongpredicate conditions, such that, if one predicate condition evaluates astrue, then other predicate conditions tend to evaluate as false.
 19. Thearticle of claim 11, wherein the optimistic selectivity assumptionsresult in estimates that predict fewer rows will be qualified by thequery.
 20. The article of claim 11, wherein the normal, pessimistic andoptimistic selectivity assumptions are weighted differently, with moreweight given to the normal selectivity assumptions and less weight givento the pessimistic and optimistic selectivity assumptions.